Upvote:6
with the flights being run by different airlines, did I give up protection from delayed flights
No. It's a single booking with Cathay and the have the responsibility to get you to your final destination.
and the right to bring more luggage on the domestic parts of the trip?
That should be spelled in the terms and conditions of your ticket. Typically the checked baggage allowance is the same for all legs of the flight. Carry-on size and weight can vary between carriers, but chances are that Cathay is more restrictive than American anyway.